Geodesic
Residuality by finite $\pi$-groups of tubular groups
Algebra i logika, Tome 63 (2024) no. 1, pp. 39-57

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A finitely generated group $G$, which acts on a tree so that all edge stabilizers are infinite cyclic groups and all vertex stabilizers are free rank $2$ Abelian groups, is called a tubular group. Every tubular group is isomorphic to the fundamental group $\pi_1(\mathcal G)$ of a suitable finite graph ${\mathcal G}$ of groups. We prove a criterion for residuality by finite $\pi$-groups of tubular groups presented by trees of groups. Also we state a criterion for residuality by finite $p$-groups of tubular groups whose corresponding graph contains one edge outside a maximal subtree.
Keywords: residuality by $\pi$-groups, residual finiteness, tubular groups. 
@article{AL_2024_63_1_a3,
     author = {F. A. Dudkin and A. V. Usikov},
     title = {Residuality by finite $\pi$-groups of tubular groups},
     journal = {Algebra i logika},
     pages = {39--57},
     publisher = {mathdoc},
     volume = {63},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2024_63_1_a3/}
}
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F. A. Dudkin; A. V. Usikov. Residuality by finite $\pi$-groups of tubular groups. Algebra i logika, Tome 63 (2024) no. 1, pp. 39-57. http://geodesic.mathdoc.fr/item/AL_2024_63_1_a3/